\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t8\_matrix\_7 (TMFUuEgAZPsRj8PiBwtiaVTE1MLvnh1AXdk)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ m1\_matrix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_matrix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_matrix\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_matrix\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k2\_finseq\_1~np\_\_2)~\\
(k2\_finseq\_1~np\_\_2)){\unicdcdcdhd}((v3\_funct\_2~X0~(k2\_finseq\_1~np\_\_2)~(k2\_finseq\_1~\\
np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_finseq\_1~\\
np\_\_2)~(k2\_finseq\_1~np\_\_2))))))){\unicdbdjdcd}((v4\_matrix\_2~X0~np\_\_2){\unicdbdjdcd}(X0=\\
k10\_finseq\_1~np\_\_2~np\_\_1))\end{array}
\label{hyp:ehedpfngbgehchjgihpfhd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k11\_matrix\_2}~{({{k12\_matrix\_2}~{X0}})}}={X0}})}}}\label{hyp:ehbdidpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_finseq\_1}~{X0}}={{k5\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{np\_\_2} \in {k4\_ordinal1}}\label{hyp:mgcdadpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k12\_matrix\_2~X0)){\unicdcdcdhd}\\
(v3\_matrix\_2~(k12\_matrix\_2~X0)))\end{array}
\label{hyp:ggdgcdpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_matrix\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_matrix\_2~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_finseq\_1~\\
(k11\_matrix\_2~X0))~(k2\_finseq\_1~(k11\_matrix\_2~X0))){\unicdcdcdhd}((v3\_funct\_2~\\
X1~(k2\_finseq\_1~(k11\_matrix\_2~X0))~(k2\_finseq\_1~(k11\_matrix\_2~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_finseq\_1~\\
(k11\_matrix\_2~X0))~(k2\_finseq\_1~(k11\_matrix\_2~X0)))))))))\end{array}
\label{hyp:egehpfngbdpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k10\_finseq\_1~X0~X1=k7\_finseq\_1~(k9\_finseq\_1~\\
X0)~(k9\_finseq\_1~X1)\end{array}
\label{hyp:egjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjded}{({{X0} \in {k4\_ordinal1}})}}}\label{hyp:egbdcdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehidpfngbgehchjgihpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k13\_matrix\_2~np\_\_2))){\unicdbdjdcd}\\
(({\unicdcdaddd} X1 .  (m1\_matrix\_2~X1~(k12\_matrix\_2~np\_\_2)){\unicdcdcdhd}((X1=X0){\unicdcdcdhd}\\
(v4\_matrix\_2~X1~(k11\_matrix\_2~(k12\_matrix\_2~np\_\_2))))){\unicdbdjdcd}(X0=\\
k10\_finseq\_1~np\_\_2~np\_\_1))\end{array}$$
\end{theorem}
\end{document}
